Details

analyze51.0ms (1.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
50%	50%	0.1%	4
50%	50%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
87.4%	12.5%	0.1%	8
87.4%	12.5%	0.1%	9
93.7%	6.2%	0.1%	10
93.7%	6.2%	0.1%	11
96.8%	3.1%	0.1%	12
96.8%	3.1%	0.1%	13
98.3%	1.6%	0.1%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample891.0ms (28.9%)

Results

681.0ms	7623×	body	128	valid
60.0ms	190×	body	2048	valid
58.0ms	219×	body	1024	valid
28.0ms	150×	body	512	valid
10.0ms	74×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify23.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

254×	`fma-neg_binary64`
112×	`fma-def_binary64`
90×	`cancel-sign-sub-inv_binary64`
48×	`sub-neg_binary64`
40×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	43	10
4	79	10
5	146	10
6	244	10
7	348	8
8	442	8
9	595	8
10	650	8
11	590	8

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 (-.f64 x y) 1/2 x)

Compiler

Compiled 31 to 18 computations (41.9% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (-.f64 x y) 1/2 x)

series4.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

4.0ms

(fma.f64 (-.f64 x y) 1/2 x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (-.f64 x y) 1/2 x)

simplify47.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

854×	`distribute-neg-out_binary64`
765×	`unsub-neg_binary64`
531×	`fma-def_binary64`
337×	`associate-l_binary64`
272×	`associate-r_binary64`

Counts

34 → 22

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	331
1	35	278
2	68	278
3	169	278
4	658	278
5	2504	278
6	5244	278

prune16.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	20	2	22
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	20	3	23

Error

0.1b

Counts

23 → 3

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (-.f64 x y) 1/2 x)
▶	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
	43.8b	(cbrt.f64 (pow.f64 (fma.f64 -1/2 y (*.f64 3/2 x)) 3))

Compiler

Compiled 301 to 183 computations (39.2% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (-.f64 x y) 1/2 x)
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
✓	0.6b	(cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))

series56.0ms (1.8%)

Counts

3 → 72

Calls

3 calls:

29.0ms

(*.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))

22.0ms

(cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))

5.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))

rewrite18.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

7.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))

4.0ms

(*.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))

1.0ms

(cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))

simplify104.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

744×	`fma-def_binary64`
497×	`cancel-sign-sub-inv_binary64`
224×	`sub-neg_binary64`
213×	`unswap-sqr_binary64`
203×	`associate-r_binary64`

Counts

165 → 234

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	343	4501
1	895	4176
2	2910	3743
3	5249	3743

prune357.0ms (11.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	432	10	442
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	433	12	445

Error

0.0b

Counts

445 → 12

Alt Table

Status	Error	Program
	31.8b	(.f64 (.f64 (*.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))) (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x))))
	31.9b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))))
▶	1.3b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 3)
	1.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (-.f64 x y) x))) 6)) (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (-.f64 x y) x)))))
	2.5b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (-.f64 x y) x))) 4) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (-.f64 x y) x))) 4)) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))))
	43.8b	(cbrt.f64 (pow.f64 (fma.f64 -1/2 y (*.f64 3/2 x)) 3))
	1.5b	(.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
	2.1b	(.f64 (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))))) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
✓	0.1b	(fma.f64 (-.f64 x y) 1/2 x)
	32.8b	(.f64 (cbrt.f64 (.f64 (fma.f64 (-.f64 x y) 1/2 x) (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
	1.7b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
	32.0b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 1/2 (-.f64 x y) x))) 3)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))

Compiler

Compiled 16301 to 10087 computations (38.1% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (-.f64 x y) 1/2 x)
	0.6b	(cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 3)

series955.0ms (30.9%)

Counts

1 → 24

Calls

1 calls:

955.0ms

(pow.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 3)

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`cube-prod_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`cbrt-prod_binary64`
6×	`unpow-prod-down_binary64`

Counts

1 → 32

Calls

1 calls:

2.0ms

(pow.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 3)

simplify83.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

636×	`fma-def_binary64`
509×	`associate-l_binary64`
492×	`associate-r_binary64`
327×	`log-prod_binary64`
261×	`exp-prod_binary64`

Counts

56 → 64

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1254
1	273	1130
2	779	1069
3	3260	749
4	4760	749
5	5002	749

prune99.0ms (3.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	154	3	157
Fresh	10	0	10
Picked	0	1	1
Done	0	1	1
Total	164	5	169

Error

0.0b

Counts

169 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (-.f64 x y) 1/2 x)
▶	12.0b	(fma.f64 (/.f64 (.f64 x (.f64 y -1/2)) y) -3 (*.f64 y -1/2))
✓	1.3b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 3)
	31.4b	(/.f64 -3/2 (/.f64 -1 x))
	31.7b	(*.f64 x (cbrt.f64 27/8))

Compiler

Compiled 3146 to 2278 computations (27.6% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (/.f64 (.f64 x (.f64 y -1/2)) y) -3 (*.f64 y -1/2))
✓	13.9b	(/.f64 (.f64 x (.f64 y -1/2)) y)

series8.0ms (0.2%)

Counts

2 → 48

Calls

2 calls:

4.0ms	(fma.f64 (/.f64 (.f64 x (.f64 y -1/2)) y) -3 (*.f64 y -1/2))
3.0ms	(/.f64 (.f64 x (.f64 y -1/2)) y)

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`

Counts

2 → 35

Calls

2 calls:

4.0ms	(/.f64 (.f64 x (.f64 y -1/2)) y)
0.0ms	(fma.f64 (/.f64 (.f64 x (.f64 y -1/2)) y) -3 (*.f64 y -1/2))

simplify71.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

887×	`times-frac_binary64`
779×	`associate-/l*_binary64`
519×	`associate-l_binary64`
305×	`associate-/r*_binary64`
263×	`associate-*l/_binary64`

Counts

83 → 65

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	82	926
1	193	595
2	773	565
3	4141	565
4	4985	565
5	4925	565

prune33.0ms (1.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	2	0	2
Picked	1	0	1
Done	2	0	2
Total	69	1	70

Error

Counts

70 → 1

Alt Table

Status	Error	Program
	0b	(fma.f64 (.f64 -1/2 x) -3 (.f64 y -1/2))

Compiler

Compiled 990 to 667 computations (32.6% saved)

regimes188.0ms (6.1%)

Accuracy

Total 0b remaining (0%)

Threshold costs 0b (0%)

Counts

55 → 1

Compiler

Compiled 3453 to 2195 computations (36.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	10	11
2	10	11

end39.0ms (1.3%)

Compiler: Compiled 30 to 24 computations (20% saved)

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	43	10
4	79	10
5	146	10
6	244	10
7	348	8
8	442	8
9	595	8
10	650	8
11	590	8

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	43	10
4	79	10
5	146	10
6	244	10
7	348	8
8	442	8
9	595	8
10	650	8
11	590	8

Details

analyze51.0ms (1.6%)

sample891.0ms (28.9%)

simplify23.0ms (0.7%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series4.0ms (0.1%)

rewrite1.0ms (0%)

simplify47.0ms (1.5%)

prune16.0ms (0.5%)

localize7.0ms (0.2%)

series56.0ms (1.8%)

rewrite18.0ms (0.6%)

simplify104.0ms (3.4%)

prune357.0ms (11.6%)

localize8.0ms (0.3%)

series955.0ms (30.9%)

rewrite3.0ms (0.1%)

simplify83.0ms (2.7%)

prune99.0ms (3.2%)

localize6.0ms (0.2%)

series8.0ms (0.2%)

rewrite9.0ms (0.3%)

simplify71.0ms (2.3%)

prune33.0ms (1.1%)

regimes188.0ms (6.1%)

simplify2.0ms (0.1%)

end39.0ms (1.3%)

Profiling

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	43	10
4	79	10
5	146	10
6	244	10
7	348	8
8	442	8
9	595	8
10	650	8
11	590	8